Ben and Jerry are standing at the center of a 134 kg merry-go-round of radius 1.30 m that is already spinning at 3.00 rad/s. They proceed to walk in opposite directions toward the edge of the merry-go-round.
If Ben reaches the edge while Jerry is halfway between the center and the edge, what will be the new angular velocity (in rad/s) of the merry-go-round? Assume Ben and Jerry can be modeled as point masses of 32.0 kg and 21.0 kg, respectively, and that the merry-go-round can be modeled as a disk rotated about its axis.
Using Angular momentum
Li = Lf
Ii*wi = If*wf
wf = wi*(Ii/If)
moment of inertia of disk = M*R^2/2
Moment of inertia of Ben/Jerry about center of disk = m*r^2
where r = distance from center
Ii = M*R^2/2 + 0 + 0
Since initially Ben And Jerry are at center, so r = 0
Ii = 134*1.30^2/2 = 113.23 kg-m^2
wi = 3 rad/sec
If = MR^2/2 + mb*rb^2 + mj*rj^2
mb = mass of ben = 32 kg
mj = mass of jerry = 21 kg
rb = distance of ben from center = R = 1.30 m
rj = distance of jerry from center = R/2 = 0.65 m
If = 134*1.30^2/2 + 32*1.30^2 + 21*0.65^2
If = 176.18 kg-m^2
wf = 3*(113.23/176.18)
wf = 1.93 rad/sec
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